The use of approximately parallel arched beams as base members for apparatuses such as rocking chairs and rocking horses is well known. Such rocking apparatuses allow the user to rock only with a forward and backward motion. Notwithstanding rocking apparatuses that have previously been disclosed, there remains a need for a stable rocking apparatus which can be rocked in all directions in the plane of an underlying support surface without the danger of easily tipping over. Such features are particularly desirable in the design and construction of riding toys for children.